Preheat oven to 325°F. In a small, heavy saucepan, stir together sugar and 5 Tbsp. water; bring to a boil over medium-high heat. Cook, washing down any sugar crystals on side of pan with a wet pastry brush, until sugar dissolves, 5 minutes. To make caramel, cook, without stirring, to a deep caramel color, 8 minutes. Pour caramel into a round 9-by- 2-inch cake pan with straight sides. Using pot holders, tilt pan to coat bottom evenly. Set aside.
In a large bowl, whisk eggs, egg whites and espresso. Stir in evaporated milk, condensed milk, vanilla extract and salt until smooth. Strain into a large glass measure. Place a roasting pan in oven, and carefully place cake pan inside roasting pan. Pour custard into cake pan. Pour simmering water into roasting pan to come halfway up sides of cake pan. Bake until jiggly and a small, sharp knife inserted into custard comes out fairly clean, 1 1/4 to 1 1/2 hours.
Carefully transfer cake pan to a rack to cool. Refrigerate, loosely covered, until cold, at least 4 hours or overnight.
Run a table knife around inside edge of cake pan and shake pan gently to loosen flan. Invert flan onto a large platter with a rim to catch caramel.